the rectangle qrst is a dilation of the rectangle qrst. what is the scale factor of the dilation? simplify…

the rectangle qrst is a dilation of the rectangle qrst. what is the scale factor of the dilation? simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.

the rectangle qrst is a dilation of the rectangle qrst. what is the scale factor of the dilation? simplify your answer and write it as a proper fraction, an improper fraction, or a whole number.

Answer

Explanation:

Step1: Find side - lengths of original and dilated rectangles

Let's consider the horizontal side of the rectangles. For rectangle $QRST$, if we consider the $x$ - coordinates of $Q(9,2)$ and $T(- 8,2)$, the length of $QT$ is $|9-(-8)|=17$. For rectangle $Q'R'S'T'$, if we consider the $x$ - coordinates of $Q'(5,1)$ and $T'(-4,1)$, the length of $Q'T'$ is $|5 - (-4)|=9$.

Step2: Calculate the scale factor

The scale factor $k$ of a dilation is given by the ratio of the length of a side of the dilated figure to the length of the corresponding side of the original figure. So, $k=\frac{\text{length of side of }Q'R'S'T'}{\text{length of side of }QRST}$. Using the horizontal sides we found above, $k = \frac{9}{17}$.

Answer:

$\frac{9}{17}$